4,向量a=(4cosx,sinx) 向量b=(siny,4cosy)向量c=(cosy,负4sinx) 若向量a与向量

向量c=(cosy,负4sinx) 应该是“=(cosy,负4siny)”吧?
1、向量b-向量2c=(siny,4cosy)-2(cosy,-4sinx)
=(siny-2cosy,4cosy+8siny)
∵向量a与向量b-向量2c垂直
∴(向量a)(向量b-向量2c)=0
即4cosx(siny-2cosy)+sinx(4cosy+8siny)
=4cosxsiny-8cosxcosy+4sinxcosy+8sinxsiny
=(4cosxsiny+4sinxcosy)-(8cosxcosy-8sinxsiny)
=4sin(x+y)-8cos(x+y)
=0
∴4sin(x+y)=8cos(x+y)
即tan(x+y)=sin(x+y)/cos(x+y)=2

2、∵tanxtany=16
∴sinxsiny=16cosxcosy
即sinx/(4cosy)=4cosx/siny
∴向量a和向量b平行

3、向量b+向量c
=(siny,4cosy)+(cosy,-4siny)
=(siny+cosy,4cosy-4siny)
∵要求绝对值向量b加向量c最大值,即为求其平方的最大值
即(siny+cosy)²+(4cosy-4siny)²
=1+2sinycosy+16-32sinycosy
=17-30sinycosy
=17-15sin(2y)
∵当sin(2y)=-1时,17-15sin(2y)有最大值32
则绝对值向量b加向量c最大值为√32=4√2